Online Appendix C

Ambiguity attitudes and surprises

Authors

Affiliations

Aljoscha Minnich

Center for Earth System Research and Sustainability (CEN), University of Hamburg

Department of Economics, University of Hamburg

Hauke Roggenkamp

Institute of Behavioral Science and Technology, University of St. Gallen

Faculty of Economics & Social Sciences, Helmut-Schmidt-University

Andreas Lange

Center for Earth System Research and Sustainability (CEN), University of Hamburg

Department of Economics, University of Hamburg

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This document explains how to reproduce the figures presented in the paper.

Install Packages

We install the following packages using the groundhog package manager to increase computational reproducibility.

if (!requireNamespace("groundhog", quietly = TRUE)) {
    install.packages("groundhog")
    library("groundhog")
}

pkgs <- c("magrittr", "data.table", "stringr", "lubridate", "knitr", "glue",
          "sandwich", "lmtest",
          "ggplot2", "ggpubr", "rstatix", "patchwork", "scales")

groundhog::groundhog.library(pkg = pkgs,
                             date = "2023-09-25")

Read Data

# data <- data.table::fread(file = "../data/processed/full.csv")
data <- readRDS(file="../data/processed/full.Rda")

data[, communication := as.factor(communication)]
data[, communication := factor(communication, levels = c("point", "both","interval"))]
data[, stage := as.factor(stage)]
data[, stage := factor(stage, levels = c("1", "2"))]

Data set

ful1<-subset(data,data$stage==1)
ful2<-subset(data,data$stage==2)

cols <- c("participant.label", "E1", "E2", "E3", "E12","E23","E13","b","a","communication","surprise")
ful1 <- ful1[, ..cols]
ful2 <- ful2[, ..cols]

fgr<-merge(ful1,ful2,by=c("participant.label","communication","surprise"))

ful1<-NULL
ful2<-NULL

#Subsets for the figures table

fgr1<-subset(fgr,fgr$surprise==TRUE & fgr$communication=="both")
fgr2<-subset(fgr,fgr$surprise==TRUE & fgr$communication=="interval")
fgr3<-subset(fgr,fgr$surprise==TRUE & fgr$communication=="point")
fgr4<-subset(fgr,fgr$surprise==FALSE & fgr$communication=="both")
fgr5<-subset(fgr,fgr$surprise==FALSE & fgr$communication=="interval")
fgr6<-subset(fgr,fgr$surprise==FALSE & fgr$communication=="point")
fgr7<-subset(fgr,fgr$surprise==TRUE)
fgr8<-subset(fgr,fgr$surprise==FALSE)

Figure OC1

To create Figure 1 (and the other figures), we create a wrapper function that we can call several times. As all the other figures presented in this document, Figure 1 consists of eight panels, that are relatively similar. We thus, save both space and sources of error by creating a wrapper function plot_bars() that creates bar plots and annotates them.

plot_bars <- function(outcome.y,outcome.x,participant.label,tmp, breaks, limits,x1,x2,x3,x4,y1,y2,y3,y4){


#percentage for graph:
p1<-scales::percent(as.numeric(table(outcome.y>outcome.x)["TRUE"]/length(unique(participant.label))),accuracy = 1)#upper percentage
p2<-scales::percent(as.numeric(table(outcome.y<outcome.x)["TRUE"]/length(unique(participant.label))),accuracy = 1)#lower percentage

#Spearman Correlation for Subtitle of graph:
ro.value<-round(cor(outcome.x, outcome.y, method = c("spearman")),2)


plot<-ggplot(data=tmp, aes(x = outcome.x, y = outcome.y)) +
  geom_count(shape=1,show.legend = FALSE)+
  theme(line = element_blank(), panel.background = element_rect(fill = "white",
                                                                colour = "white",
                                                                linewidth = 0.5, linetype = "solid"))+
  xlab(as.expression(bquote(rho~"="~.(ro.value)))) +
  ylab("") +
  geom_vline(xintercept = 0, colour = "black")+
  geom_hline(yintercept = 0, colour = "black")+
  geom_abline(intercept = 0, slope = 1, color="black", 
               linewidth=0.6)+
  scale_x_continuous(breaks = breaks, lim = limits)+
  scale_y_continuous(breaks = breaks, lim = limits)+
  geom_text(x=x1, y=y1, label="Part 1")+
  geom_text(x=x2, y=y2, label="Part 2")+
  geom_text(x=x3, y=y3, label=p1)+
  geom_text(x=x4, y=y4, label=p2)

  
  plot
  
}

top1   <- plot_bars(fgr8$b.y,fgr8$b.x,fgr8$participant.label,fgr8,seq(-1, 1, 0.5), c(-1.02, 1.02),0.9,0.3,-0.6,0.6,-0.115,1.05,0.7,-0.7)
top2  <- plot_bars(fgr7$b.y,fgr7$b.x,fgr7$participant.label,fgr7, seq(-1, 1, 0.5), c(-1.02, 1.02),0.9,0.3,-0.6,0.6,-0.115,1.05,0.7,-0.7)
middle1 <- plot_bars(fgr6$b.y,fgr6$b.x,fgr6$participant.label,fgr6, seq(-1, 1, 0.5), c(-1.02, 1.02),0.9,0.3,-0.6,0.6,-0.115,1.05,0.7,-0.7)
middle2 <- plot_bars(fgr5$b.y,fgr5$b.x,fgr5$participant.label,fgr5, seq(-1, 1, 0.5), c(-1.02, 1.02),0.9,0.3,-0.6,0.6,-0.115,1.05,0.7,-0.7)
middle3 <- plot_bars(fgr4$b.y,fgr4$b.x,fgr4$participant.label,fgr4, seq(-1, 1, 0.5), c(-1.02, 1.02),0.9,0.3,-0.6,0.6,-0.115,1.05,0.7,-0.7)
down1 <- plot_bars(fgr3$b.y,fgr3$b.x,fgr3$participant.label,fgr3, seq(-1, 1, 0.5), c(-1.02, 1.02),0.9,0.3,-0.6,0.6,-0.115,1.05,0.7,-0.7)
down2 <- plot_bars(fgr2$b.y,fgr2$b.x,fgr2$participant.label,fgr2, seq(-1, 1, 0.5), c(-1.02, 1.02),0.9,0.3,-0.6,0.6,-0.115,1.05,0.7,-0.7)
down3 <- plot_bars(fgr1$b.y,fgr1$b.x,fgr1$participant.label,fgr1, seq(-1, 1, 0.5), c(-1.02, 1.02),0.9,0.3,-0.6,0.6,-0.115,1.05,0.7,-0.7)

( (top1|top2) / (middle1 | middle2 | middle3) / (down1 | down2 | down3) & theme(legend.position = "bottom")) + plot_layout(guides = "collect")

Figure 1: Scatterplot of the ambiguity index b. The relationship between part 1 and part 2 separated by treatments with correlation coefficients and percentages above and below the diagonal.

Figure OC.2

top1   <- plot_bars(fgr8$a.y,fgr8$a.x,fgr8$participant.label,fgr8, seq(-2, 4, 1), c(-2, 4), 3.4,0.8,-1.5,1.5,-0.4,3.9,1.9,-1.9)
top2  <- plot_bars(fgr7$a.y,fgr7$a.x,fgr7$participant.label,fgr7, seq(-2, 4, 1), c(-2, 4), 3.4,0.8,-1.5,1.5,-0.4,3.9,1.9,-1.9)
middle1 <- plot_bars(fgr6$a.y,fgr6$a.x,fgr6$participant.label,fgr6, seq(-2, 4, 1), c(-2, 4), 3.4,0.8,-1.5,1.5,-0.4,3.9,1.9,-1.9)
middle2 <- plot_bars(fgr5$a.y,fgr5$a.x,fgr5$participant.label,fgr5, seq(-2, 4, 1), c(-2, 4), 3.4,0.8,-1.5,1.5,-0.4,3.9,1.9,-1.9)
middle3 <- plot_bars(fgr4$a.y,fgr4$a.x,fgr4$participant.label,fgr4, seq(-2, 4, 1), c(-2, 4), 3.4,0.8,-1.5,1.5,-0.4,3.9,1.9,-1.9)
down1 <- plot_bars(fgr3$a.y,fgr3$a.x,fgr3$participant.label,fgr3, seq(-2, 4, 1), c(-2, 4), 3.4,0.8,-1.5,1.5,-0.4,3.9,1.9,-1.9)
down2 <- plot_bars(fgr2$a.y,fgr2$a.x,fgr2$participant.label,fgr2, seq(-2, 4, 1), c(-2, 4), 3.4,0.8,-1.5,1.5,-0.4,3.9,1.9,-1.9)
down3 <- plot_bars(fgr1$a.y,fgr1$a.x,fgr1$participant.label,fgr1, seq(-2, 4, 1), c(-2, 4), 3.4,0.8,-1.5,1.5,-0.4,3.9,1.9,-1.9)

( (top1|top2) / (middle1 | middle2 | middle3) / (down1 | down2 | down3) & theme(legend.position = "bottom")) + plot_layout(guides = "collect")

Figure 2: Scatterplot of the ambiguity index a. The relationship between part 1 and part 2 separated by treatments with correlation coefficients and percentages above and below the diagonal.

Figure OC.3

top1   <- plot_bars(fgr8$E1.y,fgr8$E1.x,fgr8$participant.label,fgr8, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
top2  <- plot_bars(fgr7$E1.y,fgr7$E1.x,fgr7$participant.label,fgr7, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle1 <- plot_bars(fgr6$E1.y,fgr6$E1.x,fgr6$participant.label,fgr6, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle2 <- plot_bars(fgr5$E1.y,fgr5$E1.x,fgr5$participant.label,fgr5, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle3 <- plot_bars(fgr4$E1.y,fgr4$E1.x,fgr4$participant.label,fgr4, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down1 <- plot_bars(fgr3$E1.y,fgr3$E1.x,fgr3$participant.label,fgr3, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down2 <- plot_bars(fgr2$E1.y,fgr2$E1.x,fgr2$participant.label,fgr2, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down3 <- plot_bars(fgr1$E1.y,fgr1$E1.x,fgr1$participant.label,fgr1, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)


( (top1|top2) / (middle1 | middle2 | middle3) / (down1 | down2 | down3) & theme(legend.position = "bottom")) + plot_layout(guides = "collect")

Figure 3: Scatterplot of the matching probabilities for event E1. The relationship between part 1 and part 2 separated by treatments with correlation coefficients and percentages above and below the diagonal.

Figure OC.4

top1   <- plot_bars(fgr8$E2.y,fgr8$E2.x,fgr8$participant.label,fgr8, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
top2  <- plot_bars(fgr7$E2.y,fgr7$E2.x,fgr7$participant.label,fgr7, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle1 <- plot_bars(fgr6$E2.y,fgr6$E2.x,fgr6$participant.label,fgr6, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle2 <- plot_bars(fgr5$E2.y,fgr5$E2.x,fgr5$participant.label,fgr5, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle3 <- plot_bars(fgr4$E2.y,fgr4$E2.x,fgr4$participant.label,fgr4, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down1 <- plot_bars(fgr3$E2.y,fgr3$E2.x,fgr3$participant.label,fgr3, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down2 <- plot_bars(fgr2$E2.y,fgr2$E2.x,fgr2$participant.label,fgr2, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down3 <- plot_bars(fgr1$E2.y,fgr1$E2.x,fgr1$participant.label,fgr1, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)



( (top1|top2) / (middle1 | middle2 | middle3) / (down1 | down2 | down3) & theme(legend.position = "bottom")) + plot_layout(guides = "collect")

Figure 4: Scatterplot of the matching probabilities for event E2. The relationship between part 1 and part 2 separated by treatments with correlation coefficients and percentages above and below the diagonal.

Figure OC.5

top1   <- plot_bars(fgr8$E3.y,fgr8$E3.x,fgr8$participant.label,fgr8, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
top2  <- plot_bars(fgr7$E3.y,fgr7$E3.x,fgr7$participant.label,fgr7, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle1 <- plot_bars(fgr6$E3.y,fgr6$E3.x,fgr6$participant.label,fgr6, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle2 <- plot_bars(fgr5$E3.y,fgr5$E3.x,fgr5$participant.label,fgr5, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle3 <- plot_bars(fgr4$E3.y,fgr4$E3.x,fgr4$participant.label,fgr4, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down1 <- plot_bars(fgr3$E3.y,fgr3$E3.x,fgr3$participant.label,fgr3, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down2 <- plot_bars(fgr2$E3.y,fgr2$E3.x,fgr2$participant.label,fgr2, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down3 <- plot_bars(fgr1$E3.y,fgr1$E3.x,fgr1$participant.label,fgr1, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)


( (top1|top2) / (middle1 | middle2 | middle3) / (down1 | down2 | down3) & theme(legend.position = "bottom")) + plot_layout(guides = "collect")

Figure 5: Scatterplot of the matching probabilities for event E3. The relationship between part 1 and part 2 separated by treatments with correlation coefficients and percentages above and below the diagonal.

Figure OC.6

top1   <- plot_bars(fgr8$E12.y,fgr8$E12.x,fgr8$participant.label,fgr8, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
top2  <- plot_bars(fgr7$E12.y,fgr7$E12.x,fgr7$participant.label,fgr7, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle1 <- plot_bars(fgr6$E12.y,fgr6$E12.x,fgr6$participant.label,fgr6, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle2 <- plot_bars(fgr5$E12.y,fgr5$E12.x,fgr5$participant.label,fgr5, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle3 <- plot_bars(fgr4$E12.y,fgr4$E12.x,fgr4$participant.label,fgr4, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down1 <- plot_bars(fgr3$E12.y,fgr3$E12.x,fgr3$participant.label,fgr3, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down2 <- plot_bars(fgr2$E12.y,fgr2$E12.x,fgr2$participant.label,fgr2, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down3 <- plot_bars(fgr1$E12.y,fgr1$E12.x,fgr1$participant.label,fgr1, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)


( (top1|top2) / (middle1 | middle2 | middle3) / (down1 | down2 | down3) & theme(legend.position = "bottom")) + plot_layout(guides = "collect")

Figure 6: Scatterplot of the matching probabilities for event E12. The relationship between part 1 and part 2 separated by treatments with correlation coefficients and percentages above and below the diagonal.

Figure OC.7

top1   <- plot_bars(fgr8$E13.y,fgr8$E13.x,fgr8$participant.label,fgr8, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
top2  <- plot_bars(fgr7$E13.y,fgr7$E13.x,fgr7$participant.label,fgr7, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle1 <- plot_bars(fgr6$E13.y,fgr6$E13.x,fgr6$participant.label,fgr6, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle2 <- plot_bars(fgr5$E13.y,fgr5$E13.x,fgr5$participant.label,fgr5, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle3 <- plot_bars(fgr4$E13.y,fgr4$E13.x,fgr4$participant.label,fgr4, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down1 <- plot_bars(fgr3$E13.y,fgr3$E13.x,fgr3$participant.label,fgr3, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down2 <- plot_bars(fgr2$E13.y,fgr2$E13.x,fgr2$participant.label,fgr2, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down3 <- plot_bars(fgr1$E13.y,fgr1$E13.x,fgr1$participant.label,fgr1, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)


( (top1|top2) / (middle1 | middle2 | middle3) / (down1 | down2 | down3) & theme(legend.position = "bottom")) + plot_layout(guides = "collect")

Figure 7: Scatterplot of the matching probabilities for event E13. The relationship between part 1 and part 2 separated by treatments with correlation coefficients and percentages above and below the diagonal.

Figure OC.8

top1   <- plot_bars(fgr8$E23.y,fgr8$E23.x,fgr8$participant.label,fgr8, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
top2  <- plot_bars(fgr7$E23.y,fgr7$E23.x,fgr7$participant.label,fgr7, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle1 <- plot_bars(fgr6$E23.y,fgr6$E23.x,fgr6$participant.label,fgr6, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle2 <- plot_bars(fgr5$E23.y,fgr5$E23.x,fgr5$participant.label,fgr5, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
middle3 <- plot_bars(fgr4$E23.y,fgr4$E23.x,fgr4$participant.label,fgr4, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down1 <- plot_bars(fgr3$E23.y,fgr3$E23.x,fgr3$participant.label,fgr3, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down2 <- plot_bars(fgr2$E23.y,fgr2$E23.x,fgr2$participant.label,fgr2, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)
down3 <- plot_bars(fgr1$E23.y,fgr1$E23.x,fgr1$participant.label,fgr1, seq(0, 100, 50), c(0, 101), 90,15,15,90,5,100,80,20)



( (top1|top2) / (middle1 | middle2 | middle3) / (down1 | down2 | down3) & theme(legend.position = "bottom")) + plot_layout(guides = "collect")

Figure 8: Scatterplot of the matching probabilities for event E23. The relationship between part 1 and part 2 separated by treatments with correlation coefficients and percentages above and below the diagonal.